# ForAll

ForAll[x,expr]

represents the statement that expr is True for all values of .

ForAll[x,cond,expr]

states that expr is True for all x satisfying the condition cond.

ForAll[{x1,x2,},expr]

states that expr is True for all values of all the xi.

# Details

• ForAll[x,expr] can be entered as xexpr. The character can be entered as fa or \[ForAll]. The variable x is given as a subscript.
• ForAll[x,cond,expr] can be entered as x,condexpr.
• In StandardForm, ForAll[x,expr] is output as xexpr.
• ForAll[x,cond,expr] is output as x,condexpr.
• ForAll can be used in such functions as Reduce, Resolve, and FullSimplify.
• The condition cond is often used to specify the domain of a variable, as in xIntegers.
• ForAll[x,cond,expr] is equivalent to ForAll[x,Implies[cond,expr]].
• ForAll[{x1,x2,},] is equivalent to .
• The value of in ForAll[x,expr] is taken to be localized, as in Block.

# Examples

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## Basic Examples(1)

This states that for all , is positive:

 In[1]:=
 Out[1]=

Use Resolve to get a condition on real parameters for which the statement is true:

 In[2]:=
 Out[2]=

Reduce gives the condition in a solved form:

 In[3]:=
 Out[3]=